Generalized sharp Hardy type and Caffarelli-Kohn-Nirenberg type inequalities on Riemannian manifolds
2009 ◽
Vol 40
(4)
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pp. 401-413
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Keyword(s):
We prove generalized Hardy's type inequalities with sharp constants and Caffarelli-Kohn-Nirenberg inequalities with sharp constants on Riemannian manifolds $M$. When the manifold is Euclidean space we recapture the sharp Caffarelli-Kohn-Nirenberg inequality. By using a double limiting argument, we obtain an inequality that implies a sharp Hardy's inequality, for functions with compact support on the manifold $M $ (that is, not necessarily on a punctured manifold $ M \backslash \{ x_0 \} $ where $x_0$ is a fixed point in $M$). Some topological and geometric applications are discussed.
1987 ◽
Vol 105
(1)
◽
pp. 265-274
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Keyword(s):
Keyword(s):
1999 ◽
Vol 127
(9)
◽
pp. 2745-2754
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Keyword(s):
2008 ◽
Vol 11
(01)
◽
pp. 21-31
◽
1998 ◽
pp. 331-348
Keyword(s):